{
  "id": "2405.17045",
  "version": "v1",
  "published": "2024-05-27T11:01:47.000Z",
  "updated": "2024-05-27T11:01:47.000Z",
  "title": "A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms",
  "authors": [
    "Daniele Galli"
  ],
  "comment": "58 pages",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "We investigate Ruelle-Pollicott resonances of Anosov diffeomorphisms with respect to the measure of maximal entropy. We highlight a profound connection between resonances and eigenvalues of the action induced by the dynamics on de Rham cohomology. We finally exploit this relation to get information about the Ruelle-Pollicott asymptotics of the correlation function and establish a cohomological bound for the speed of mixing of Anosov diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-27T11:01:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A25",
      "37D20",
      "37C30",
      "14F40"
    ],
    "keywords": [
      "anosov diffeomorphisms",
      "ruelle-pollicott resonances",
      "cohomological approach",
      "correlation function",
      "ruelle-pollicott asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}